Producing a Refined Control Mesh for Generating a Smooth Surface of an Object

2. The computer-implemented method of claim 1, wherein the extraordinary point is one of many control vertices in the obtained polygonal control mesh, and wherein the extraordinary point is a non-uniform point in the polygonal control mesh.

5. The computer-implemented method of claim 1, wherein the obtained polygonal control mesh includes an N-gon, the one or more subdivisions are two or more subdivisions, and wherein the subdividing comprises an initial subdivision as a first subdivision of the two or more subdivisions, and the extraordinary point is created inside the N-gon by the initial subdivision.

6. The computer-implemented method of claim 5, wherein the initial subdivision comprises locating the extraordinary point in a face of the N-gon and an initial set of edge points defining the eigen polyhedron, wherein the extraordinary point in the face of the N-gon and the initial set of edge points is determined in accordance with a Non-Uniform Rational Catmull-Clark Subdivision (NURCCS) rule.

7. The computer-implemented method of claim 1, wherein the subdividing is compatible with Non-Uniform Rational Catmull-Clark Subdivision (NURCCS) and Non-Uniform Rational Basis Spline (NURBS) surfaces.

8. The computer-implemented method of claim 1, wherein the one or more subdivisions comprises at least one subdivision of control polygon faces in an extraordinary region of the polygonal control mesh but not in a region adjacent to the extraordinary region.

10. The computer-implemented method of claim 1, wherein subdividing the polygonal control mesh includes subdivision of the faces around the extraordinary point into four faces, and subdividing at least a set of faces that are first level neighbors to the faces around the extraordinary point into two faces each, wherein at least the set of faces is subdivided into two faces each according to a knot insertion rule so as not to change a shape of the smooth surface.

11. The computer-implemented method of claim 10, wherein the generating of the smooth surface comprises generating patches for polygons of the refined control mesh that correspond to at least second level neighbor faces of faces around the extraordinary point after subdividing.

13. The system of claim 12, wherein the extraordinary point is one of many control vertices in the obtained polygonal control mesh, and wherein the extraordinary point is a non-uniform point in the polygonal control mesh.

14. The system of claim 12, wherein the obtained polygonal control mesh includes an N-gon, the one or more subdivisions are two or more subdivisions, and wherein the instructions configured to cause the data processing apparatus to subdivide comprise instructions configured to cause the data processing apparatus to subdivide an initial subdivision as a first subdivision of the two or more subdivisions, the extraordinary point is created inside the N-gon by the initial subdivision, and wherein the initial subdivision comprises locating the extraordinary point in a face of the N-gon and an initial set of edge points defining the eigen polyhedron, wherein the extraordinary point in the face of the N-gon and the initial set of edge points are determined in accordance with a Non-Uniform Rational Catmull-Clark Subdivision (NURCCS) rule, and wherein the subdividing is compatible with Non-Uniform Rational Catmull-Clark Subdivision (NURCCS) and Non-Uniform Rational Basis Spline (NURBS) surfaces.

16. The system of claim 12, wherein the instructions configured to cause the data processing apparatus to subdivide the polygonal control mesh include instructions to subdivide the faces around the extraordinary point into four faces, and subdivide at least a set of faces that are first level neighbors to the faces around the extraordinary point into two faces each, wherein at least the set of faces is subdivided into two faces each according to a knot insertion rule so as not to change a shape of the smooth surface, wherein the instructions configured to cause the data processing apparatus to generate the smooth surface comprise instructions configured to cause the data processing apparatus to generate patches for polygons of the refined control mesh that correspond to at least second level neighbor faces of faces around the extraordinary point after subdividing.

18. The computer-readable medium of claim 17, wherein the extraordinary point is one of many control vertices in the obtained polygonal control mesh, and wherein the extraordinary point is a non-uniform point in the polygonal control mesh.

19. The computer-readable medium of claim 17, wherein the obtained polygonal control mesh includes an N-gon, the one or more subdivisions are two or more subdivisions, and wherein the subdividing comprises an initial subdivision as a first subdivision of the two or more subdivisions, and the extraordinary point is created inside the N-gon by the initial subdivision.

20. The computer-readable medium of claim 17, wherein the initial subdivision comprises locating the extraordinary point in a face of the N-gon and an initial set of edge points defining the eigen polyhedron, wherein the extraordinary point in the face of the N-gon and the initial set of edge points is determined in accordance with a Non-Uniform Rational Catmull-Clark Subdivision (NURCCS) rules, wherein the subdividing is compatible with Non-Uniform Rational Catmull-Clark Subdivision (NURCCS) and Non-Uniform Rational Basis Spline (NURBS) surfaces.